Bayesian learning consistently combines expert knowledge, theoretical models of reality, and data into a posterior distribution that expresses belief in various values of unknown quantities.

It online updates adaptive systems. Its classical theory [1] serves non-trivial applications [2], tunes algorithms [3], fuses knowledge even with atypical models [4], and works with data-based forgetting [5].

[1] Peterka, V.: Bayesian system identification. In: P. Eykhoff (ed.) Trends and Progress in System Identification, 239–304, 1981.
[2] Tichý O., Šmídl V., Hofman R., Šindelářová Kateřina, Hýža M., Stohl A.:  Bayesian inverse modelling and source location of an unintended 131I release in Europe in the fall of 2011, Atmospheric Chemistry and Physics 17(20):12677-12696, 2017.
[3] Kárný M.:  Towards on-line tuning of adaptive-agent’s multivariate meta-parameter, International Journal of Machine Learning and Cybernetics 12(9): 2717-2731, 2021.
[4] Kuklišová Pavelková L., Jirsa L., Quinn A.:  Fully probabilistic design for knowledge fusion between Bayesian filters under uniform disturbances, Knowledge-Based System 238, 2022.
[5] Kárný M.: Optimized geometric pooling of probabilities for information fusion and forgetting, Automatica 177, 2025.

Contact: Miroslav Kárný